Thank you to all who sent very helpful advice (or who wrote wondering what the heck I was talking about!). Necessary and sufficient conditions was actually what I was after. I just needed to revisit it. Begging the question falls in there. And Gödel/Schrödinger etc for the last bit. Intensionality (with the "s") was helpful as well: unicorns, the round square etc. On Thu, Mar 24, 2011 at 11:34 AM, Gary Antonick <gantonick@gmail.com> wrote:
Feels like you guys are the village elders and I'm the kid who's gotten into some trouble with something simple. Am hoping for basic logic advice on structuring "reasons" — perhaps something from AI or rhetoric. I post puzzles online periodically and several days ago ran a Gardner classic: Why Are Manhole Covers Round? Readers have suggested tons of reasons: won't fall into the hole, etc. I'm now trying to structure the reasons and even potentially reject the question and the idea that there can be a "reason" in the logical sense. Any suggestions would be great. Cheers, Gary Structuring Reasons 1. rejecting the question First of all, I think the question "Why Are Manhole Covers Round?" is itself invalid because it's begging the question. Am wondering if anyone familiar with logic might confirm this. I was thinking of using this analogy. Why are racecar tires rubber? Why not wood? Romans used wood. Someone might say wood is inflexible and too slippery. Wait. If wood were the only option for tires then the sport of racecar driving as we know it wouldn't exist. 2. parallel and serial causes Second, am hoping someone might suggest a method for structuring reasons where there's not a necessary and sufficient condition. I'll use the racecar example again: Racecar x crashes in race y. Why did racecar x crash? It was going too fast. OK. If it had been going slower it would not have crashed? Well, no. It had also been struck from the side.. and the track was slippery. These seem to be in parallel.. that is, they have similar status. There's always one more. Hydra heads. Then there's a list of reasons that seem to be in series. 1. cars were invented 2. car racing developed 3. car racing conditions/rules give rise to/allow crashes 4. racecar x created 5. racecar x is in good condition 6. racecar x participates in race y Take out one of these and the car doesn't crash. But they aren't really "reasons." 3. rejecting causality: emergent results Then there's the final outcome: racecar x [crashes, not crashes], which has me wonder if "reasons" can only be assigned to conditions and not to outcomes. That is, the track was wet because it rained. No rain, no wet.